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   "cell_type": "code",
   "execution_count": null,
   "id": "9001a6ec-4ed8-47d9-84b8-1e909067d94c",
   "metadata": {},
   "outputs": [],
   "source": [
    "线性回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7f74830e-39d6-49a6-84a3-a36f6bf6e3f8",
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   "outputs": [],
   "source": [
    "训练数据\n",
    "     在机器学习术语⾥，该数据集被称为训练数据集（training data set）或训练集（training set），⼀栋房屋被称为⼀个样本\n",
    "（sample），其真实售出价格叫作标签（label），⽤来预测标签的两个因素叫作特征（feature）。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "601af11c-877e-4820-9c99-29f08eceebef",
   "metadata": {},
   "outputs": [],
   "source": [
    "损失函数\n",
    "在机器学习⾥，将衡量误差的函数称为损失函数（loss function）。这⾥使⽤的平⽅误差函数也称为平⽅损失（square loss）。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8616e71b-5812-466e-930a-1ef06b3b2969",
   "metadata": {},
   "outputs": [],
   "source": [
    "优化算法\n",
    "    当模型和损失函数形式较为简单时，上⾯的误差最⼩化问题的解可以直接⽤公式表达出来。这类解叫作解析解（analytical solution）。\n",
    "本节使⽤的线性回归和平⽅误差刚好属于这个范畴。\n",
    "然⽽，⼤多数深度学习模型并没有解析解，只能通过优化算法有限次迭代模型参数来尽可能降低损失函数的值。这类解\n",
    "叫作数值解（numerical solution）。\n",
    "    ⼩批量随机梯度下降（mini-batch stochastic gradient descent）在深度学习中被⼴泛使⽤。\n",
    "它的算法很简单：先选取⼀组模型参数的初始值，如随机选取；接下来对参数进⾏数据样本所组成的⼩批量（mini-batch） ，然后求⼩批量中数据样本的平均损失有关模型参数的导数\n",
    "（梯度），最后⽤此结果与预先设定的⼀个正数的乘积作为模型参数在本次迭代的减⼩量。\n",
    " 代表每个⼩批量中的样本个数（批量⼤⼩，batch size）， 称作学习率（learning\n",
    "rate）并取正数。需要强调的是，这⾥的批量⼤⼩和学习率的值是⼈为设定的，并不是通过模型训练学\n",
    "出的，因此叫作超参数（hyperparameter）。我们通常所说的“调参”指的正是调节超参数，例如通过\n",
    "反复试错来找到超参数合适的值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "be8875b2-a93a-469a-beba-820f26ebd74f",
   "metadata": {},
   "outputs": [],
   "source": [
    "神经网络计算方法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2a0ee01d-8ae8-46f6-86b8-b1d0639323f8",
   "metadata": {},
   "outputs": [],
   "source": [
    "输⼊分别为x1和x2，因此输⼊层的输⼊个数为2。输⼊个数也叫特征数或特征向量维度。\n",
    "神经⽹络的输出 作为线性回归的输出，即 。由于输⼊层并不涉及计算，按照惯例，神经⽹络的层数为1。所以，线性回归是⼀个单层神经⽹络。输出层中负责计算 的单元⼜叫神经元。\n",
    "在线性回归中输出层中的神经元和输⼊层中各个输⼊完全连接。因此，这⾥的输出层⼜叫全连接层（fully-connected layer）或稠密层（dense layer）。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "47a779cd-18e7-4080-9bbd-2e581703ffd4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "from time import time\n",
    "a = torch.ones(1000)\n",
    "b = torch.ones(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1e97cd65-a1d8-4b51-a915-c0cad0a6524c",
   "metadata": {},
   "outputs": [],
   "source": [
    "向量相加，元素逐一做加法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "fb10d998-5be0-459b-a132-bf99927cca2f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.024888038635253906\n"
     ]
    }
   ],
   "source": [
    "start = time()\n",
    "c = torch.zeros(1000)\n",
    "for i in range(1000):\n",
    " c[i] = a[i] + b[i]\n",
    "print(time() - start)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "272eb7cd-cdc8-44d8-ba28-c3800ec39616",
   "metadata": {},
   "outputs": [],
   "source": [
    "矢量加法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1371c38c-f3fd-4e06-b653-dd61b99659f6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.000997781753540039\n"
     ]
    }
   ],
   "source": [
    "start = time()\n",
    "d = a + b\n",
    "print(time() - start)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cc2be723-f770-4600-b389-3fff5ad1c4c5",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "⼴播机制\n",
    "在不进行显式重复数组内容的情况下，广播机制会自动地将一个较小的数组扩展到与另一个数组形状一致，从而能够执行元素级的运算。这种机制通常用于矩阵、向量与标量之间的运算。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "933e709d-bf72-448b-a246-cf43e589b5e1",
   "metadata": {},
   "outputs": [],
   "source": [
    "线性回归从零实现"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "d4eb1468-e29e-4710-899d-f90f61fada2e",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import torch\n",
    "from IPython import display\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "09b2f105-b46f-45b0-b5d3-92469f8d9dc3",
   "metadata": {},
   "outputs": [],
   "source": [
    "生成数据集"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "4066dd24-b0f2-4e51-8013-81ec77fb22a7",
   "metadata": {},
   "outputs": [],
   "source": [
    "num_inputs = 2\n",
    "num_examples = 1000\n",
    "true_w = [2, -3.4]\n",
    "true_b = 4.2\n",
    "features = torch.from_numpy(np.random.normal(0, 1, (num_examples, \n",
    "num_inputs)))\n",
    "labels = true_w[0] * features[:, 0] + true_w[1] * features[:, 1] + true_b\n",
    "labels += torch.from_numpy(np.random.normal(0, 0.01, \n",
    "size=labels.size()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "982e5825-f589-4001-b321-557a49153f40",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([-0.4627,  0.4825], dtype=torch.float64) tensor(1.6319, dtype=torch.float64)\n"
     ]
    }
   ],
   "source": [
    "print(features[0], labels[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "552e5d2f-415b-4a2a-9d3c-06a21ca835c7",
   "metadata": {},
   "outputs": [],
   "source": [
    "在同一个文件夹中调用d2lzh_pytorch py文件"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "7e4b7b76-7c3f-49b5-9a31-c3dcb9e1e76e",
   "metadata": {},
   "outputs": [
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   "source": [
    "import sys\n",
    "sys.path.append(\"..\")\n",
    "from d2lzh_pytorch import * \n",
    "set_figsize()\n",
    "plt.scatter(features[:, 1].numpy(), labels.numpy(), 1);\n",
    "plt.show()"
   ]
  },
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   "execution_count": null,
   "id": "0843ed50-170a-4055-afc8-f17a1dd1cd15",
   "metadata": {},
   "outputs": [],
   "source": [
    "数据处理"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "65d2a98c-0f46-44f1-a4af-5b1ff683d5cf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[-0.5646,  0.0786],\n",
      "        [ 0.8288, -0.9482],\n",
      "        [ 0.8372, -0.8355],\n",
      "        [-1.0635,  0.6352],\n",
      "        [-0.2105, -0.4914],\n",
      "        [ 0.0810, -0.9227],\n",
      "        [-1.1605,  0.4951],\n",
      "        [-0.7787,  0.0076],\n",
      "        [ 1.8033, -1.0416],\n",
      "        [-0.4250,  0.4129]], dtype=torch.float64) tensor([ 2.8100,  9.0850,  8.7245, -0.0813,  5.4425,  7.4921,  0.2104,  2.6117,\n",
      "        11.3516,  1.9537], dtype=torch.float64)\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "sys.path.append(\"..\")\n",
    "from d2lzh import * \n",
    "\n",
    "batch_size = 10\n",
    "for X, y in data_iter(batch_size, features, labels):\n",
    " print(X, y)\n",
    " break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "37329be5-24c7-48f7-999e-33da30e029f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "初始化模型参数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9a70b6b8-fe87-4282-bd90-1a80d0ae5c6b",
   "metadata": {},
   "outputs": [],
   "source": [
    "权重初始化成均值为0、标准差为0.01的正态随机数，偏差则初始化成0。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7652dd31-bbaf-484b-a5ec-2ef64cf4bf8d",
   "metadata": {},
   "outputs": [],
   "source": [
    "w = torch.tensor(np.random.normal(0, 0.01, (num_inputs, 1)), \n",
    "dtype=torch.float32)\n",
    "b = torch.zeros(1, dtype=torch.float32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "df004052-84b9-4875-b3e1-6679cfb732f1",
   "metadata": {},
   "outputs": [],
   "source": [
    "需要对这些参数进行求导来迭代这些参数值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b7e4b9e1-e95d-4850-84a3-93df1853d7ed",
   "metadata": {},
   "outputs": [],
   "source": [
    "w.requires_grad_(requires_grad=True)\n",
    "b.requires_grad_(requires_grad=True) "
   ]
  }
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